- Volume 11, Number 6 (2005), 1059-1092.
On the convergence of the spectral empirical process of Wigner matrices
It is well known that the spectral distribution Fn of a Wigner matrix converges to Wigner's semicircle law. We consider the empirical process indexed by a set of functions analytic on an open domain of the complex plane including the support of the semicircle law. Under fourth-moment conditions, we prove that this empirical process converges to a Gaussian process. Explicit formulae for the mean function and the covariance function of the limit process are provided.
Bernoulli, Volume 11, Number 6 (2005), 1059-1092.
First available in Project Euclid: 16 January 2006
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Bai, Z.D.; Yao, J. On the convergence of the spectral empirical process of Wigner matrices. Bernoulli 11 (2005), no. 6, 1059--1092. doi:10.3150/bj/1137421640. https://projecteuclid.org/euclid.bj/1137421640